Question 14 5pt In the options below, there is only one polynomial that is irreducible over...
Question 15 6 pts The polynomial g(x) = 2 + x + x?is irreducible over Z3, and B is a root of g(x). What is an equivalent expression for 86 as a linear function of ß? O 2 + 2B O 2 + B 2B 01+B 01+2B ОВ
Preview Activity 14.1. In previous investigations, we defined irreducible polynomials and showed that irreducible polynomials in polynomial rings over fields play the same role as primes play in Z. In this investigation we will explore some methods to determine when a polynomial is irreducible, with a special emphasis on polynomials with coefficients in C, R, and Q. To begin, we will review the definition and a simple case. Let F be a field. (a) Give a formal definition of what...
4. Show that the polynomial g(x) = x++x+1 is irreducible over Z2. In the quotient ring Z2[x]/(g(x)) let S = x+(g(x)), so that Z2[x]/(g(x)) = Z2(). Express 85 and (82 +1)-1 in the form a + b8 + 082 +883, where a, b, c, d e Z2.
6 pts Question 16 The polynomial g(x) = 2 + x + x?is irreducible over Zz, and B is a root of g(x). What is an equivalent expression for 1 + 87 as a power of B? O B3 O 06
Let k be a field of positive characteristic p, and let f(x)be an irreducible polynomial. Prove that there exist an integer d and a separable irreducible polynomial fsep (2) such that f(0) = fsep (2P). The number p is called the inseparable degree of f(c). If f(1) is the minimal polynomial of an algebraic element a, the inseparable degree of a is defined to be the inseparable degree of f(1). Prove that a is inseparable if and only if its...
SECTION 4.3 Polynomial Division; The Factor the polynomial function f(x). Then solve the equation f(x) = 0. 39, f(x) =x3 + 4x2 + x-6 40. fx) 5x - 2x 24 41, f(x) =x3-6x2 + 3x+10 42. f(x)-x3 + 2x2-13x + 10 43, f(x) = x3-x2-14x + 24 44.f(x) = x3-3x2 In Ex given. a): Fi b) C in gi - L 二 10x +24ー丁only, this one d) C gi ase 45' f(x) =x4-7x3 + 9x2 + 27x-54 plecs( 46, f(x)...
I just need 23, I have 21 and 22, but since it is a parts question this is context. Thank you! Question 21 1 pts Recall the power series expansion 1 = 1 - x + x2 – 23 + ... on the interval (-1, 1). Use the given expansion to derive a power series expansion for 1772 Show at least 3 non-zero terms. • 1-x2 + x4 - x +... 0 - 1 + x2-x4 + x + ......
please Solve the question with excel solver Solve the question with excel solver URBAN PLANNING - URBAN RENEWAL MODEL Example 2.4.6 on page 70 of Taha's book Decision variables: XI-Number of units of single-family homes x2 - Number of units of double-family homes x3 = Number of units of triple-family homes x4 - Number of units of quadruple-family homes xs = Number of old homes to be demolished XS Maximize z=1000 x1 + 1900 x2 +2700 x3 +3400 x4 Subject...
(1 point) Compare and discuss the long-run behaviors of the functions below. In each blank, enter either the constant or the polynomial that the rational function behaves like as x + Foo: 23 – 3 1. x4 – 3 f(x) = ar — x2 – 3 23 – 8 , and h(x) = 23 – 8' x3 – 8' f(x) will behave like the function y = as x + +0. help (formulas) g(x) will behave like the function y...
other options needed info QUESTION 10 If the profit per dozen changes to: Sweatshirt - F profit = $85 Sweatshirt - B/F profit = $120 T-shirt - F profit = $40 T-shirt - B/F profit = $80 What happens with the LP model of this problem? Max Z-90x1125x2+45x3+66x4 subject to 85X1 + 120X2 + 40X3.BOX4 572 3X1 + 3X2 X3 X4 S 1200 36X1 +48X225x3 +35X4 S 25000 X1 + X2 X3 X4 S 500 X1 X2 X3 X40 Max...